

class 					__lowercase  :





							"""simple docstring"""

							def __init__(					self						)		->       Tuple:
														A      :					Dict      		=					{}




							def       snake_case			(					self						)		->       None:
														print(self.vertex						)
														for i in self.vertex:
																					print(__UpperCAmelCase    ,						''' -> '''    ,						''' -> '''.join([str(__UpperCAmelCase						) for j in self.vertex[i]]						)						)




							def       snake_case			(					self    ,						__UpperCAmelCase    ,						__UpperCAmelCase						)		->       None:
														# check if vertex is already present,
														if from_vertex in self.vertex:
																					self.vertex[from_vertex].append(__UpperCAmelCase						)
														else:
																					# else make a new vertex
																					A      :					Optional[Any]      		=					[to_vertex]




							def       snake_case			(					self						)		->       None:
														# visited array for storing already visited nodes
														A      :					Dict      		=					[False] * len(self.vertex						)

														# call the recursive helper function
														for i in range(len(self.vertex						)						):
																					if not visited[i]:
																												self.dfs_recursive(__UpperCAmelCase    ,						__UpperCAmelCase						)






							def       snake_case			(					self    ,						__UpperCAmelCase    ,						__UpperCAmelCase						)		->       None:
														# mark start vertex as visited
														A      :					List[str]      		=					True

														print(__UpperCAmelCase    ,						end=''' '''						)

														# Recur for all the vertices that are adjacent to this node
														for i in self.vertex:
																					if not visited[i]:
																												self.dfs_recursive(__UpperCAmelCase    ,						__UpperCAmelCase						)


if __name__ == "__main__":
		lowercase			:				str   =     Graph()
		g.add_edge(0, 1)
		g.add_edge(0, 2)
		g.add_edge(1, 2)
		g.add_edge(2, 0)
		g.add_edge(2, 3)
		g.add_edge(3, 3)

		g.print_graph()
		print("DFS:")
		g.dfs()

		# OUTPUT:
		# 0  ->  1 -> 2
		# 1  ->  2
		# 2  ->  0 -> 3
		# 3  ->  3
		# DFS:
		#  0 1 2 3









from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403






def        snake_case__		(    lowerCamelCase_     ,				lowerCamelCase_     ,				lowerCamelCase_ = "x"     ,				lowerCamelCase_ = 10**-10     ,				lowerCamelCase_ = 1     ,				):
							A      :					int      		=					symbols(lowerCamelCase_		)
							A      :					List[str]      		=					lambdify(lowerCamelCase_     ,				lowerCamelCase_		)
							A      :					Tuple      		=					lambdify(lowerCamelCase_     ,				diff(lowerCamelCase_     ,				lowerCamelCase_		)		)

							A      :					Optional[int]      		=					starting_point

							while True:
														if diff_function(lowerCamelCase_		) != 0:
																					A      :					Union[str, Any]      		=					prev_guess - multiplicity * func(lowerCamelCase_		) / diff_function(
																					    lowerCamelCase_		)
														else:
																					raise ZeroDivisionError('''Could not find root'''		) from None

														# Precision is checked by comparing the difference of consecutive guesses
														if abs(next_guess - prev_guess		) < precision:
																					return next_guess

														A      :					Tuple      		=					next_guess


# Let's Execute
if __name__ == "__main__":
		# Find root of trigonometric function
		# Find value of pi
		print(F"The root of sin(x) = 0 is {newton_raphson('sin(x)', 2)}")

		# Find root of polynomial
		# Find fourth Root of 5
		print(F"The root of x**4 - 5 = 0 is {newton_raphson('x**4 -5', 0.4 +5J)}")

		# Find value of e
		print(
		    "The root of log(y) - 1 = 0 is ",
		    F"{newton_raphson('log(y) - 1', 2, variable='y')}",
		)

		# Exponential Roots
		print(
		    "The root of exp(x) - 1 = 0 is",
		    F"{newton_raphson('exp(x) - 1', 10, precision=0.0_05)}",
		)

		# Find root of cos(x)
		print(F"The root of cos(x) = 0 is {newton_raphson('cos(x)', 0)}")






